A grand potential approach to phase-field modeling of rapid solidification

2014 ◽  
Vol 39 (2) ◽  
Author(s):  
Denis A. Danilov ◽  
Vladimir G. Lebedev ◽  
Peter K. Galenko
Keyword(s):  
Binary System ◽  
Rapid Solidification ◽  
Phase Field ◽  
Binary Systems ◽  
Local Equilibrium ◽  
Phase Field Model ◽  
Irreversible Thermodynamics ◽  
Governing Equations ◽  
Potential Approach ◽  
Grand Potential

Abstract.Rapid solidification occurs under large driving force of transformation from the metastable undercooled liquid phase to the stable crystalline state. Using a formalism of extended irreversible thermodynamics, a phase-field model of rapid solidification in binary systems is derived. An entropy approach together with a grand potential density of a binary system is used to obtain the main governing equations of the model. Special attention is paid to equations of a rapidly solidifying binary system which are accompanied by essential deviations from local equilibrium in the transport of the conservative variables (such as inner energy and mass) and in the dynamics of non-conservative variables (such as phase field). The obtained equations are analyzed and compared with recent models and outcomes based on the grand potential approach to solidification.

scholarly journals Modelling of Microstructure Evolution during Laser Processing of Intermetallic Containing Ni-Al Alloys

Metals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 1051
Author(s):  
Mohammad Amin Jabbareh ◽  
Hamid Assadi
Keyword(s):  
Additive Manufacturing ◽  
Rapid Solidification ◽  
Microstructure Evolution ◽  
Phase Field ◽  
Laser Processing ◽  
Field Model ◽  
Phase Field Model ◽  
Intermetallic Phases ◽  
Al Alloy ◽  
Kinetic Effects

There is a growing interest in laser melting processes, e.g., for metal additive manufacturing. Modelling and numerical simulation can help to understand and control microstructure evolution in these processes. However, standard methods of microstructure simulation are generally not suited to model the kinetic effects associated with rapid solidification in laser processing, especially for material systems that contain intermetallic phases. In this paper, we present and employ a tailored phase-field model to demonstrate unique features of microstructure evolution in such systems. Initially, the problem of anomalous partitioning during rapid solidification of intermetallics is revisited using the tailored phase-field model, and the model predictions are assessed against the existing experimental data for the B2 phase in the Ni-Al binary system. The model is subsequently combined with a Potts model of grain growth to simulate laser processing of polycrystalline alloys containing intermetallic phases. Examples of simulations are presented for laser processing of a nickel-rich Ni-Al alloy, to demonstrate the application of the method in studying the effect of processing conditions on various microstructural features, such as distribution of intermetallic phases in the melt pool and the heat-affected zone. The computational framework used in this study is envisaged to provide additional insight into the evolution of microstructure in laser processing of industrially relevant materials, e.g., in laser welding or additive manufacturing of Ni-based superalloys.

Solute trapping and solute drag in a phase-field model of rapid solidification

1998 ◽  
Vol 58 (3) ◽  
pp. 3436-3450 ◽  
Author(s):  
N. A. Ahmad ◽  
A. A. Wheeler ◽  
W. J. Boettinger ◽  
G. B. McFadden
Keyword(s):  
Rapid Solidification ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Solute Drag ◽  
Solute Trapping

Phase Field Modeling of Solute Trapping in a Al-Sn Alloy during Rapid Solidification

2014 ◽  
Vol 794-796 ◽  
pp. 740-745 ◽  
Author(s):  
Xiong Yang ◽  
Li Jun Zhang ◽  
Yong Du
Keyword(s):  
Rapid Solidification ◽  
Phase Field ◽  
Field Model ◽  
Kinetic Equations ◽  
Phase Field Model ◽  
Interface Velocity ◽  
Interface Energy ◽  
Phase Field Simulation ◽  
Solute Trapping ◽  
Field Simulation

During rapid solidification, interfaces are often driven far from equilibrium and the "solute trapping" phenomenon is usually observed. Very recently, a phase field model with finite interface dissipation, in which separate kinetic equations are assigned to each phase concentration instead of an equilibrium partitioning condition, has been newly developed. By introducing the so-called interface permeability, the phase field model with finite interface dissipation can nicely describe solute trapping during solidification in the length scale of micrometer. This model was then applied to perform a phase field simulation in a Al-Sn alloy (Al-0.2 at.% Sn) during rapid solidification. A simplified linear phase diagram was constructed for providing the reliable driving force and potential information. The other thermophysical parameters, such as interface energy and diffusivities, were directly taken from the literature. As for the interface mobility, it was estimated via a kinetic relationship in the present work. According to the present phase field simulation, the interface velocity increases as temperature decreases, resulting in the enhancement of solute trapping. Moreover, the simulated solute segregation coefficients in Al-0.2 at.% Sn can nicely reproduce the experimental data.

scholarly journals Experimental and numerical modeling for flattening and rapid solidification with crystallization behavior of supersonic ceramic droplets

2020 ◽  
Author(s):  
Y. Wang ◽  
Y Bai ◽  
K Wu ◽  
J Zhou ◽  
M G Shen ◽  
...  
Keyword(s):  
Rapid Solidification ◽  
Phase Field ◽  
Crystallization Behavior ◽  
Field Model ◽  
Solidification Rate ◽  
Phase Field Model ◽  
Oriented Attachment ◽  
Navier Stokes ◽  
Columnar Grains ◽  
And Migration

Abstract Successive impingement of supersonic droplets after refining in plasma jet usually forms a fine-lamellar structured coating with high mechanical properties. However, the comprehensive process (such as flattening, rapid solidification and crystallization) of high-velocity impact of refined droplets is difficult to understand. In this study, an experimental study showed that the content of refinement droplets reached to 90 % and displayed the multi-scale equiaxed grains morphology at extremely rapid solidification rate. Phase-field model revealed a hybrid coalescence growth of oriented attachment and migration of grains boundary under the dynamic temperature gradient. Furthermore, an optimized numerical model that consisted of the Navier-Stokes and energy balance equations coupled with the Cahn-Hilliard and phase-field model for growth orientation of grains was developed to accurately reproduce the comprehensive process of refined supersonic droplets. The size distribution and crystallographic orientation of columnar grains for single or two flattened droplets were in a good agreement with the experimental results. The interface between two-flattened droplets exhibited an epitaxial growth of columnar grains. This optimized model can be an effective method in predicting the flattening and solidification with crystallization behavior of droplets during plasma spraying.

A Phase-Field Model for Rapid Solidification with Non-Equilibrium Solute Diffusion

2015 ◽  
Vol 817 ◽  
pp. 14-20
Author(s):  
Hai Feng Wang ◽  
Cun Lai ◽  
Xiao Zhang ◽  
Kuang Wang ◽  
Feng Liu
Keyword(s):  
Rapid Solidification ◽  
Phase Field ◽  
Growth Velocity ◽  
Field Model ◽  
Phase Field Model ◽  
Solute Diffusion ◽  
Current Phase ◽  
Diffusion Velocity ◽  
Good Agreement ◽  
Non Equilibrium

Since the growth velocity can be comparable with or even larger than the solute diffusion velocity in the bulk phases, modeling of rapid solidification with non-equilibrium solute diffusion becomes quite an important topic. In this paper, an effective mobility approach was proposed to derive the current phase field model (PFM). In contrast with the previous PFMs that were derived by the so-called kinetic energy approach, diffusionless solidification happens not only in the bulk phases but also inside the interface when the growth velocity is equal to the solute diffusion velocity in liquid. A good agreement between the model predictions and experimental results is obtained for rapid solidification of Si-9at.%As alloy.

Special Cases of the Grand Potential Phase Field Model

2021 ◽  
pp. 51-80
Author(s):  
Nikolas Provatas ◽  
Tatu Pinomaa ◽  
Nana Ofori-Opoku
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Special Cases ◽  
Grand Potential
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